Abstract: An operational space control solution is provided for rigid-body dynamical systems such as humanoid or legged robots. The solution includes an operational space controller that decomposes rigid body dynamics into task space dynamics and null space dynamics. Then, for systems that are fully actuated and have constraints, the controller provides control signals defining task space torques and null space torques for each actuator (e.g., a motor for a rotary joint between two rigid links). In some embodiments, a minimum torque vector is determined such that the controller is a minimum-torque operational space controller. For systems that are underactuated, task and null space dynamics are again considered, and underactuation is addressed by using null space forces to indirectly apply torque at passive degrees of freedom such as at active joints to create task-irrelevant motion that moves passive joints to facilitate task performance by the robot or rigid-body dynamical system.

Abstract: An operational space control solution is provided for rigid-body dynamical systems such as humanoid or legged robots. The solution includes an operational space controller that decomposes rigid body dynamics into task space dynamics and null space dynamics. Then, for systems that are fully actuated and have constraints, the controller provides control signals defining task space torques and null space torques for each actuator (e.g., a motor for a rotary joint between two rigid links). In some embodiments, a minimum torque vector is determined such that the controller is a minimum-torque operational space controller. For systems that are underactuated, task and null space dynamics are again considered, and underactuation is addressed by using null space forces to indirectly apply torque at passive degrees of freedom such as at active joints to create task-irrelevant motion that moves passive joints to facilitate task performance by the robot or rigid-body dynamical system.